Strong asymptotic freeness of Haar unitaries in quasi-exponential dimensional representations - ANR - Agence nationale de la recherche
Preprints, Working Papers, ... Year : 2024

Strong asymptotic freeness of Haar unitaries in quasi-exponential dimensional representations

Abstract

We prove almost sure strong asymptotic freeness of i.i.d. random unitaries with the following law: sample a Haar unitary matrix of dimension $n$ and then send this unitary into an irreducible representation of $U(n)$. The strong convergence holds as long as the irreducible representation arises from a pair of partitions of total size at most $n^{\frac{1}{24}-\varepsilon}$ and is uniform in this regime. Previously this was known for partitions of total size up to $\asymp\log n/\log\log n$ by a result of Bordenave and Collins.
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Dates and versions

hal-04726591 , version 1 (08-10-2024)

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Michael Magee, Mikael de la Salle. Strong asymptotic freeness of Haar unitaries in quasi-exponential dimensional representations. 2024. ⟨hal-04726591⟩
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